Cost–benefit modelling for reliability growth

Decisions during the reliability growth development process of engineering equipment involve trade-offs between cost and risk. However slight, there exists a chance an item of equipment will not function as planned during its specified life. Consequently the producer can incur a financial penalty. To date, reliability growth research has focussed on the development of models to estimate the rate of failure from test data. Such models are used to support decisions about the effectiveness of options to improve reliability. The extension of reliability growth models to incorporate financial costs associated with ‘unreliability’ is much neglected. In this paper, we extend a Bayesian reliability growth model to include cost analysis. The rationale of the stochastic process underpinning the growth model and the cost structures are described. The ways in which this model can be used to support cost–benefit analysis during product development are discussed and illustrated through a simple case.     

Synthesis of enantiomeric-pure cyclohexenyl nucleoside building blocks for oligonucleotide synthesis

Lipases were used for the resolution of (±) (4aR, 7R, 8aS)-2-phenyl-4a,7,8,8a-tetrahydro-4H-1,3-benzodioxine. This separation was carried out on preparative scale and used for the synthesis of eight phosphoramidites of cyclohexenyl nucleosides (d- and l-series).     

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).     

Correction to: On Webs of Maximum Rank (Geom. Dedicata 31 (1989), 19–35)

We correct an error in Example (3.4) in Geom. Dedicata 31 (1989), 19–35.     

Synthesis of all diastereomeric methyl 2,5-anhydro-3-deoxy-hexonates: precursors to C-2-deoxynucleosides and THF-templated γ- and δ-amino acids

Efficient syntheses of all diastereomers of methyl 2,5-anhydro-3-deoxy-hexonate from mannono- or gulono-lactones provide precursors for C-nucleosides of 2-deoxyribose and for THF-templated γ- and δ-amino acids.     

A local characterization of simply-laced crystals

We provide a simple list of axioms that characterize the crystal graphs of integrable highest weight modules for simply-laced quantum Kac-Moody algebras.

     

Analysis of some combination-overtone infrared bands of SO3

Several new infrared absorption bands for ³²S¹⁶O₃ have been measured and analyzed. The principal bands observed were ν₁+ν₂ (at 1561 cm⁻¹), ν₁+ν₄ (at 1594 cm⁻¹), ν₃+ν₄ (at 1918 cm⁻¹), and 3ν₃ (at 4136 cm⁻¹). Except for 3ν₃, these bands are very complicated because of (a) the Coriolis coupling between ν₂ and ν₄, (b) the Fermi resonance between ν₁ and 2ν₄, (c) the Fermi resonance between ν₁ and 2ν₂, (d) ordinary l-type resonance that couples levels that differ by 2 in both the k and l quantum numbers, and (e) the vibrational l-type resonance between the A₁^′ and A₂^′ levels of ν₃+ν₄. The unraveling of the complex pattern of these bands was facilitated by a systematic approach to the understanding of the various interactions. Fortunately, previous work on the fundamentals permitted good estimates of many constants necessary to begin the assignments and the fit of the measurements. In addition, the use of hot band transitions accompanying the ν₃ band was an essential aid in fitting the ν₃+ν₄ transitions since these could be directly observed for only one of four interacting states. From the hot band analysis we find that the A₁^′ vibrational level is 3.50 cm⁻¹ above the A₂^′ level, i.e., r₃₄=1.75236(7) cm⁻¹. In the case of the 3ν₃ band, the spectral analysis is straightforward and a weak Δk=±2, Δl₃=±2 interaction between the l₃=1 and l₃=3 substates locates the latter A₁^′ and A₂^′ “ghost” states 22.55(4) cm⁻¹ higher than the infrared accessible l₃=1 E^′ state.     

3,4‐[2,2‐Bis(methoxyethoxymethoxymethyl)propylenedithio]‐3′,4′‐(ethylenedithio)tetrathiafulvalene: a spiro‐substituted BEDT–TTF analogue

The crystal structure of the title compound [systematic name: 2‐(1,3‐dithiolo[4,5‐b][1,4]dithiin‐2‐ylidene)‐6,6‐bis(methoxyethoxymethoxymethyl)‐1,3‐dithiolo[4,5‐b][1,4]dithiepine], C₂₁H₃₀O₆S₈, a spiro‐substituted BEDT–TTF analogue [BEDT–TTF is bis(ethylenedithio)tetrathiafulvalene], has a strongly bent heterocyclic framework. The seven‐membered ring adopts a pseudo‐chair conformation with notably widened ring bond angles, especially at the methylene C atoms [119.49 (11) and 117.60 (11)°]. The axial side chain adopts an extended conformation, but the equatorial side chain curls back on itself and the O atom nearest the ring system is involved in three short contacts to H atoms (2.45–2.53 Å). The molecules pack in centrosymmetrically related pairs, which are isolated from each other by columns of the polyether side chains. This study emphasizes the ease of distortion of the neutral bis(propylenedithio)tetrathiafulvalene ring structure, and how the need to accommodate side chains can easily override the tendency of these donor systems to form stacks in the crystalline state.     

Monofunctionalised resorcinarenes

A convenient methodology for introducing single functional groups to the lower rim of resorcinarenes is described. The methodology allows for very convenient differential protection or derivatisation of the upper and lower rims, and a wide range of functional groups (alcohol, carboxylic acid, thiol, amine, carbamate, alkyl halide) can be incorporated as a single unit at the lower rim, opening up the way to further modification at this point and generally widening the scope for further utilising resorcinarenes. Furthermore, our approach has enabled us to link two resorcinarenes together to form novel resorcinarene dimers.